Republican presidential candidate Herman Cain directly confronted allegations on Tuesday that he had sexually harassed women, saying his latest accuser had lied and promising to continue his campaign.

Addressing the controversy before a throng of reporters in suburban Phoenix, Cain said he had no recollection of ever meeting Sharon Bialek, the woman who went public Monday and accused him of groping her in a car after the two dined together in Washington 14 years ago. Cain called her account "baseless, bogus and false" and said Bialek and three other women who have accused him of sexual harassment are part of a coordinated effort to attack his character and derail his campaign.

"We are not going to allow Washington or politics to deny me the opportunity to represent this great nation," Cain said, adding that he would be willing to take a lie-detector test. "As far as these accusations causing me to back off and maybe withdraw from this presidential primary race — ain't gonna happen."

The controversy over the charges escalated just minutes before Cain's news conference, when one of the previously anonymous women accusing him of inappropriate behavior decided to reveal her name after it appeared on news sites. She urged the other accusers to hold a news conference with her.

Karen Kraushaar, 55, now a communications official for the Treasury Department's inspector general for tax administration, filed a claim of sexual harassment against Cain when he headed the National Restaurant Association and she was an employee there in the 1990s. She received a payment when she left the organization, but Cain, who disputed the allegations at the time, was not a party to the agreement.

"The reason sexual harassment is so difficult to prove is that workplace sexual predators try to make sure the victim is alone when the harassment takes place," Kraushaar wrote in e-mail after Cain's news conference.

"Though reliving the matter is extremely painful, it is now no longer a private matter but a matter of public interest," she said, adding that if her employer allows, she will appear with other women who have accused Cain.

Cain decided to address the public directly after Bialek delivered her accusations Monday.

At her news conference, Bialek, a 50-year-old single mother who worked briefly in the restaurant association's Chicago office, said Cain was driving her back to her hotel after their dinner when he pulled the car over, pushed his hand up her skirt and pushed her head down toward his crotch. She said she had asked to meet him at the urging of her then-boyfriend to seek Cain's help finding work after losing her job at the association.

It was the first time one of Cain's accusers had allowed her name to be used or had appeared in public. And the graphic nature of the allegations removed the possibility that Cain's accusers could have misunderstood his sense of humor, as some of Cain's supporters had suggested.

The account prompted strong reaction from a number of politicians, including some of Cain's rivals for the Republican presidential nomination.

In an interview with ABC News on Tuesday, former Massachusetts Gov. Mitt Romney called the allegations "disturbing" and said that "they're going to have to be addressed seriously."

Former House Speaker Newt Gingrich, in a separate interview with ABC, said: "Clearly Herman Cain has to answer the charges, he has to do so in a way that's convincing, and I think that's unavoidable. He owes her that, and he also owes the American people that."

Polls continue to show Cain at the top of the field in the GOP presidential contest, effectively tied for first place with Romney.

"We don't elect a president on rumor and innuendo and allegation," said Thad Altman, a state senator in Florida and a co-chairman of Cain's campaign there. "It's so easy for people to step forward and say things. I think the truth will come out in the long term. I'm not concerned in any way shape or form."

At his news conference, Cain refused to utter Bialek's name. The former Godfather's Pizza executive said, "I don't even know who this lady is," and he described her as a "troubled woman" — a reference, apparently, to her financial difficulties, which include two bankruptcies and a federal tax lien.

Cain appeared at the news conference alongside his lawyer, Atlanta-based L. Lin Wood, who has represented other falsely accused suspects, including Richard Jewell and Rep. Gary Condit, D-Calif.

"I have known you for 46 years," Cain said his wife told him. "That doesn't even sound like anything you would ever do to anyone."

He added: "Sexual harassment is a very serious charge. Throughout my career, I have had nothing but the utmost respect for any and all women, as well as those that have worked under my leadership."

Sharon Bialek

Went public Monday and accused Cain of groping her in a car after the two dined together in Washington 14 years ago. She was the first woman to accuse Cain publicly.

Cain's response: Cain and his supporters have sharply questioned both Bialek's version of events and her motives. A Cain spokesman cast her as a "woman with a long history of severe financial difficulties.'' Bialek has denied that she was paid to come forward.

Karen Kraushaar

Had remained anonymous in her accusations against Cain. Filed a claim of sexual harassment against Cain when he headed the National Restaurant Association and she was an employee there in the 1990s. She received a payment when she left the organization, but Cain, who disputed the allegations at the time, was not a party to the agreement.

Cain's response: Said that Kraushaar's claims were "found to be baseless."